ALEX Classroom Resource

  

Algebra I Module 1, Topic D: Creating Equations to Solve Problems

  Classroom Resource Information  

Title:

 Algebra I Module 1, Topic D: Creating Equations to Solve Problems

URL:

 https://www.engageny.org/resource/algebra-i-module-1-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Topic D, students are formally introduced to the modeling cycle through problems that can be solved by creating equations and inequalities in one variable, systems of equations, and graphing (N-Q.1, A-SSE.1, A-CED.1, A-CED.2, A-REI.3). The End-of-Module Assessment follows Topic D.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
4 ) Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [N-Q1]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.Q.HS.4- Using real world models, express quantities of measurement to the given precision. (limited to measurements of length (inch, 1/2 inch, 1/4 inch), weight (pounds, kilograms (tenth of a unit), volume (cup, 1/2 cup, 1/4 cup, 1/3 cup, liter), temperature (degree), velocity (mph, kmph).
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
4. Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.

Example: Interpret the accrued amount of investment P(1 + r)t , where P is the principal and r is the interest rate, as the product of P and a factor depending on time t.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Make sense of algebraic expressions by identifying structures within the expression which allow them to rewrite it in useful ways to assist in the solution of given problems.
  • Interpret the meaning of the parts of an expression. For example, see that 3 + (x-2)2 is a sum of a constant and a square, that the square contains the expression x-2, and that the value of the expression is always greater than 3.
  • Justify their selection of a form for an expression by explaining which features of the expression are revealed by the particular form and how these features aid in resolving a problem situation.
Teacher Vocabulary:
  • Linear expression
  • Quadratic expression
  • Exponential expression
  • Equivalent expressions
Knowledge:
Students know:
  • How to recognize the parts of linear, quadratic and exponential expressions and what each part represents.
  • When one form of an algebraic expression is more useful than an equivalent form of that same expression to solve a given problem.
  • That one or more parts of an expression can be viewed as a single entity.
Skills:
Students are able to:
  • Use algebraic properties to produce equivalent forms of the same expression by recognizing underlying mathematical structures.
  • Interpret expressions in terms of a context.
  • View one or more parts of an expression as a single entity and determine the impact parts of the expression have in terms of the context.
Understanding:
Students understand that:
  • Making connections among the parts of an expression reveals the roles of important mathematical features of a problem.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.4.1: Define linear, quadratic and exponential functions.
ALGI.4.2: Classify an expression as linear, quadratic or exponential from a table.
ALGI.4.3: Classify an expression as linear, quadratic or exponential from an equation.
ALGI.4.4: Classify an expression as linear, quadratic or exponential from a graph.
ALGI.4.5: Define terms, factors, and coefficients.
ALGI.4.6: Identify factors in linear, exponential and quadratic expressions.
ALGI.4.7: Identify coefficients in linear, exponential and quadratic expressions.
ALGI.4.8: Identify terms in linear, exponential and quadratic expressions.
ALGI.4.9: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient).
ALGI.4.10: Recognize one or more parts of an exponential expression as a single entity.
ALGI.4.11: Recognize one or more parts of a quadratic expression as a single entity.
ALGI.4.12: Recognize one or more parts of a linear expression as a single entity.

Prior Knowledge Skills:
  • Recognize ordered pairs.
  • Identify ordered pairs.
  • Recognize linear equations.
  • Recall how to solve problems using the distributive property.
  • Define linear functions, nonlinear functions, slope, and y-intercept.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.4 Identify an algebraic expression involving addition or subtraction to represent a real-world problem.

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
11. Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a contextual situation that may include linear, quadratic, exponential, or rational functional relationships in one variable.
  • Model the relationship with equations or inequalities and solve the problem presented in the contextual situation for the given variable.
Teacher Vocabulary:
  • Variable
  • Equation
  • Inequality
  • Solution Set
  • Identity
  • No solution for a given domain
  • Approximate solutions
Knowledge:
Students know:
  • When the situation presented in a contextual problem is most accurately modeled by a linear, quadratic, exponential, or rational functional relationship.
Skills:
Students are able to:
  • Write equations in one variable that accurately model contextual situations.
Understanding:
Students understand that:
  • Features of a contextual problem can be used to create a mathematical model for that problem.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.11.1: Solve the equation represented by the real-world situation.
ALGI.11.2: Set up an equation to represent the given situation, using correct mathematical operations and variables.
ALGI.11.3: Given a contextual situation, interpret and defend the solution in the context of the original problem.
ALGI.11.4: Define equation, expression, variable, equality and inequality.
ALGI.11.5: Create inequalities with one variable (Exponential, Quadratic, Linear).
ALGI.11.6: Create equalities with one variable (Exponential, Quadratic, Linear).
ALGI.11.7: Solve two-step equations and inequalities.
ALGI.11.8: Solve one-step equations and inequalities using the four basic operations.
ALGI.11.9: Compare and contrast equations and inequalities.
ALGI.11.10: Recognize inequality symbols including greater than, less than, greater than equal to and less than equal to.

Prior Knowledge Skills:
  • Test the found number or number set for accuracy by substitution.
  • Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
  • Define equation, inequality, and variable.
  • Convert mathematical terms to mathematical symbols and numbers.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.11 Select an equation or inequality involving one operation (limit to addition or subtraction) with one variable that represents a real-world problem. Solve the equation.
Tags: algebra, data, equations, expressions, formulas, graphs, inequalities, units, variable
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Comments

There are four lessons on this topic.

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Author: Hannah Bradley
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